Do convolutional neural networks also have recurrent connections?
You are right. I think you are just misinterpreting the part of the sentence ('specifically LSTMs'). LSTMs are an example of a popular type of RNN.
RNNs and CNNs are different architectures but they can be used together.

Here is another sentence with the same structure:


  It is clear than dogs, specifically corgis, and cats are very common in online memes.